Question

preform the indicated operation. be sure to rationalize the denominator when necessary.make sure to simplify as much as possible and givw the exact answer (this means NO decimals since decimals is rounding!)
square root of 8 - square root of 32

Answer 1

To simplify the expression \(\sqrt{8} - \sqrt{32}\), we first simplify each square root.

1. **Simplify \(\sqrt{8}\)**:
\[
\sqrt{8} = \sqrt{4 \times 2} = \sqrt{4} \cdot \sqrt{2} = 2\sqrt{2}
\]

2. **Simplify \(\sqrt{32}\)**:
\[
\sqrt{32} = \sqrt{16 \times 2} = \sqrt{16} \cdot \sqrt{2} = 4\sqrt{2}
\]

Now, substitute these simplified square roots back into the original expression:
\[
\sqrt{8} - \sqrt{32} = 2\sqrt{2} - 4\sqrt{2}
\]

Next, combine the like terms:
\[
2\sqrt{2} - 4\sqrt{2} = (2 - 4)\sqrt{2} = -2\sqrt{2}
\]

Thus, the exact answer is:
\[
\boxed{-2\sqrt{2}}
\]